Consider \((II)\) .
Now we fix \(M \ge M _0 (\epsilon )\) .
By Corollary 5.4 in [1]}, there is \(t_0 ( \epsilon , M)\)  such that for all \(t \ge t_0 ( \epsilon , M)\)  and all \(x\) ,
\( |P ( X_{M} (t) \le x ) - P(X_{M} \le x) | \le \epsilon /2.\) 
